diff --git a/pkg/statistics/handle/bootstrap.go b/pkg/statistics/handle/bootstrap.go
index 272078ca764ff..885db2cf17fae 100644
--- a/pkg/statistics/handle/bootstrap.go
+++ b/pkg/statistics/handle/bootstrap.go
@@ -44,6 +44,11 @@ const initStatsStep = int64(500)
 
 var maxTidRecord MaxTidRecord
 
+// GetMaxTidRecordForTest gets the max tid record for test.
+func GetMaxTidRecordForTest() int64 {
+	return maxTidRecord.tid.Load()
+}
+
 // MaxTidRecord is to record the max tid.
 type MaxTidRecord struct {
 	mu  sync.Mutex
@@ -81,7 +86,7 @@ func (h *Handle) initStatsMeta4Chunk(is infoschema.InfoSchema, cache statstypes.
 	maxTidRecord.mu.Lock()
 	defer maxTidRecord.mu.Unlock()
 	if maxTidRecord.tid.Load() < maxPhysicalID {
-		maxTidRecord.tid.Store(physicalID)
+		maxTidRecord.tid.Store(maxPhysicalID)
 	}
 }
 
diff --git a/pkg/statistics/handle/handletest/initstats/load_stats_test.go b/pkg/statistics/handle/handletest/initstats/load_stats_test.go
new file mode 100644
index 0000000000000..37d0c45a9d030
--- /dev/null
+++ b/pkg/statistics/handle/handletest/initstats/load_stats_test.go
@@ -0,0 +1,104 @@
+// Copyright 2024 PingCAP, Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package initstats
+
+import (
+	"context"
+	"fmt"
+	"testing"
+
+	"github.com/pingcap/tidb/pkg/config"
+	"github.com/pingcap/tidb/pkg/parser/model"
+	"github.com/pingcap/tidb/pkg/statistics/handle"
+	"github.com/pingcap/tidb/pkg/statistics/handle/types"
+	"github.com/pingcap/tidb/pkg/testkit"
+	"github.com/stretchr/testify/require"
+)
+
+func TestConcurrentlyInitStatsWithMemoryLimit(t *testing.T) {
+	restore := config.RestoreFunc()
+	defer restore()
+	config.UpdateGlobal(func(conf *config.Config) {
+		conf.Performance.LiteInitStats = false
+		conf.Performance.ConcurrentlyInitStats = true
+	})
+	handle.IsFullCacheFunc = func(cache types.StatsCache, total uint64) bool {
+		return true
+	}
+	testConcurrentlyInitStats(t)
+}
+
+func TestConcurrentlyInitStatsWithoutMemoryLimit(t *testing.T) {
+	restore := config.RestoreFunc()
+	defer restore()
+	config.UpdateGlobal(func(conf *config.Config) {
+		conf.Performance.LiteInitStats = false
+		conf.Performance.ConcurrentlyInitStats = true
+	})
+	handle.IsFullCacheFunc = func(cache types.StatsCache, total uint64) bool {
+		return false
+	}
+	testConcurrentlyInitStats(t)
+}
+
+func testConcurrentlyInitStats(t *testing.T) {
+	store, dom := testkit.CreateMockStoreAndDomain(t)
+	tk := testkit.NewTestKit(t, store)
+	tk.MustExec("use test")
+	tk.MustExec("set global tidb_analyze_column_options='ALL'")
+	tk.MustExec("create table t1 (a int, b int, c int, primary key(c))")
+	tk.MustExec("insert into t1 values (1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,7,8)")
+	tk.MustExec("analyze table t1")
+	for i := 2; i < 10; i++ {
+		tk.MustExec(fmt.Sprintf("create table t%v (a int, b int, c int, primary key(c))", i))
+		tk.MustExec(fmt.Sprintf("insert into t%v select * from t1", i))
+		tk.MustExec(fmt.Sprintf("analyze table t%v all columns", i))
+	}
+	h := dom.StatsHandle()
+	is := dom.InfoSchema()
+	h.Clear()
+	require.Equal(t, h.MemConsumed(), int64(0))
+	require.NoError(t, h.InitStats(context.Background(), is))
+	for i := 1; i < 10; i++ {
+		tbl, err := is.TableByName(context.Background(), model.NewCIStr("test"), model.NewCIStr(fmt.Sprintf("t%v", i)))
+		require.NoError(t, err)
+		stats, ok := h.StatsCache.Get(tbl.Meta().ID)
+		require.True(t, ok)
+		for _, col := range stats.GetColSlice() {
+			require.True(t, col.IsAllEvicted())
+			require.False(t, col.IsFullLoad())
+		}
+	}
+	for i := 1; i < 10; i++ {
+		tk.MustQuery(fmt.Sprintf("explain select * from t%v where a = 1", i)).CheckNotContain("pseudo")
+	}
+	for i := 1; i < 10; i++ {
+		tk.MustQuery(fmt.Sprintf("explain select * from t%v where b = 1", i)).CheckNotContain("pseudo")
+	}
+	for i := 1; i < 10; i++ {
+		tk.MustQuery(fmt.Sprintf("explain select * from t%v where c >= 1", i)).CheckNotContain("pseudo")
+	}
+	for i := 1; i < 10; i++ {
+		tbl, err := is.TableByName(context.Background(), model.NewCIStr("test"), model.NewCIStr(fmt.Sprintf("t%v", i)))
+		require.NoError(t, err)
+		stats, ok := h.StatsCache.Get(tbl.Meta().ID)
+		require.True(t, ok)
+		for _, col := range stats.GetColSlice() {
+			require.True(t, col.IsFullLoad())
+			require.False(t, col.IsAllEvicted())
+		}
+	}
+	require.Equal(t, int64(126), handle.GetMaxTidRecordForTest())
+}